Details

sample26.0ms

Algorithm

intervals

Results

12.0ms	94×	body	1280	valid
4.0ms	128×	body	80	valid
2.0ms	22×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.4b	(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 38

Calls

2 calls:

0.0ms	(atan (+ N 1.0))
3.0ms	(- (atan (+ N 1.0)) (atan N))

series11.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
10.0ms	(- (atan (+ N 1.0)) (atan N))

simplify45.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	129	365
1	345	264
2	1480	254
3	5001	198

prune70.0ms

Filtered

44 candidates to 27 candidates (61.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize5.0ms

Local error

Found 1 expressions with local error:

0.8b	(atan2 1.0 (fma N (+ N 1.0) 1))

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 9

Calls

1 calls:

0.0ms

(atan2 1.0 (fma N (+ N 1.0) 1))

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

(atan2 1.0 (fma N (+ N 1.0) 1))

simplify91.0ms

Algorithm

egg-herbie

Counts

12 → 12

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	57
1	32	50
2	55	50
3	70	50
4	89	50
5	143	50
6	567	50
7	1779	50
8	5001	50

prune25.0ms

Filtered

12 candidates to 9 candidates (75.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.7b

localize7.0ms

Local error

Found 4 expressions with local error:

0.8b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.8b	(atan2 1.0 (fma N (+ N 1.0) 1))
16.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
16.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 48

Calls

4 calls:

0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
1.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
11.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
11.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify169.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 6 (40.0ms)

Iter	Nodes	Cost
0	37	296
1	62	276
2	100	276
3	148	276
4	341	276
5	975	276
6	3911	274
7	5001	274

prune127.0ms

Filtered

60 candidates to 42 candidates (70.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(atan2 1.0 (fma N (+ N 1.0) 1))
16.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
16.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
16.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
11.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
11.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify171.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 6 (43.0ms)

Iter	Nodes	Cost
0	37	330
1	62	314
2	100	314
3	148	314
4	341	314
5	975	314
6	3911	311
7	5001	311

prune164.0ms

Filtered

66 candidates to 45 candidates (68.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

regimes20.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample699.0ms

Algorithm

intervals

Results

380.0ms	2887×	body	1280	valid
123.0ms	4093×	body	80	valid
63.0ms	595×	body	640	valid
23.0ms	273×	body	320	valid
9.0ms	152×	body	160	valid